Let $A$ be set of all real numbers and $R$ be a relation on $A$ defined by $R=\{(a,b): 1+ab>0\}$, then relation $R$ is

For the function $f(x) = |x-1| + |x-2| + |x-3|$

Match the LIST-I with LIST-II

	LIST-I Function $f(x) =$		LIST-II For Interval
A.	$-3x + 6$	I.	$x \geq 3$
B.	$-x + 4$	II.	$x < 1$
C.	$x$	III.	$1 \leq x < 2$
D.	$3x - 6$	IV.	$2 \leq x < 3$

Choose the correct answer from the options given below:

Let L be the set of all lines in a plane and R be the relation on set L defined by $R = \{(L_1, L_2): L_1 \perp L_2\}$ Then R is

(A) an equivalence Relation

(B) a symmetric Relation

(C) not a transitive Relation

(D) a reflexive Relation

Choose the correct answer from the options given below:

The signum function $f:R\to R$, defined by

$f(x)=\begin{cases}-1, & x<0\\0, & x=0\\1, & x>0\end{cases}$ is: (Where R is set of real numbers)

Let N be set of natural numbers, then the function $f: \mathbb{N} \rightarrow \mathbb{N}$, defined by

$f(x) = \begin{cases} \frac{n+1}{2} & \text{, if } n \text{ is odd} \\ \frac{n}{2} & \text{, if } n \text{ is even} \end{cases}$, is

Let $f : R \to R$ defined by $f(x) = 2x^3 - 7$ for $x \in R$. Then :

(A) $f$ is one-one function

(B) $f$ is many to one function

(C) $f$ is bijective function

(D) $f$ is into function

Choose the correct answer from the options given below :

For the functions $f(x) = x^2$ and $g(x) = x^3$, which of the following statements are TRUE?

[where N is the set of natural numbers and Z is the set of integers]

(A) $f: N \to N$ is one-one but not onto.

(B) $f: Z \to Z$ is neither one-one nor onto.

(C) $g: N \to N$ is one-one but not onto.

(D) $g: Z \to Z$ is one-one but not onto.

Choose the correct answer from the options given below: